Framing U-Net via Deep Convolutional Framelets: Application to Sparse-view CT (1708.08333v3)

Abstract: X-ray computed tomography (CT) using sparse projection views is a recent approach to reduce the radiation dose. However, due to the insufficient projection views, an analytic reconstruction approach using the filtered back projection (FBP) produces severe streaking artifacts. Recently, deep learning approaches using large receptive field neural networks such as U-Net have demonstrated impressive performance for sparse- view CT reconstruction. However, theoretical justification is still lacking. Inspired by the recent theory of deep convolutional framelets, the main goal of this paper is, therefore, to reveal the limitation of U-Net and propose new multi-resolution deep learning schemes. In particular, we show that the alternative U- Net variants such as dual frame and the tight frame U-Nets satisfy the so-called frame condition which make them better for effective recovery of high frequency edges in sparse view- CT. Using extensive experiments with real patient data set, we demonstrate that the new network architectures provide better reconstruction performance.

• The paper introduces Dual Frame and Tight Frame U-Net architectures that satisfy frame conditions to better recover high-frequency details in sparse-view CT.
• It demonstrates improved reconstruction quality with enhanced PSNR and SSIM scores using a deep convolutional framelet framework.
• The study offers actionable insights for reducing radiation exposure while mitigating artifacts in medical imaging.

Framing U-Net via Deep Convolutional Framelets: Application to Sparse-view CT

The paper "Framing U-Net via Deep Convolutional Framelets: Application to Sparse-view CT" explores an innovative approach to overcome the limitations of traditional U-Net in the context of sparse-view computed tomography (CT). The research primarily focuses on reducing radiation dose by minimizing the number of projection views, which, however, introduces severe reconstruction artifacts.

Background and Motivation

Sparse-view CT aims to reduce radiation exposure, but the filtered back projection (FBP) method, commonly used for reconstruction, suffers from streaking artifacts due to insufficient data. This has led to various approaches, including compressed sensing techniques, that minimize artifacts albeit with high computational costs.

With recent advancements in deep learning, architectures like U-Net have shown promise in CT reconstruction tasks. Such neural networks, characterized by large receptive fields, can effectively address globalized artifacts present in sparse-view CT. However, the theoretical understanding of U-Net’s ability to handle such inverse problems is still lacking.

Deep Convolutional Framelets

The authors utilize the mathematical framework of deep convolutional framelets to analyze the U-Net architecture. This framework links low-rank Hankel matrix representations with convolutional signal processing, offering insights into the network's ability to capture the underlying structure of data for effective reconstruction.

Frame Conditions and Limitations of Standard U-Net

A critical aspect discussed is the "frame condition", which the standard U-Net architecture does not satisfy, leading to an overemphasis on low frequency components and resultant blurring artifacts. The paper proposes two alternatives: the Dual Frame U-Net and the Tight Frame U-Net, each designed to satisfy the frame condition thereby improving reconstruction performance, particularly in recovering high-frequency details.

Proposed Architectures

1. Dual Frame U-Net: This design incorporates an additional by-pass connection in the low-resolution path. By doing so, it compensates for the missing high-frequency information, thus better aligning with the frame condition. However, this architecture is noted for having a larger noise amplification factor.
2. Tight Frame U-Net: This employs orthogonal wavelet frames, specifically utilizing the Haar wavelet transform to maintain tight frame conditions. The additional high-pass path allows for enhanced recovery of high-frequency signals with minimal noise amplification.

Experimental Results and Implications

The paper includes extensive empirical evaluations using real patient data to assess the performance of these architectures. Both Dual Frame and Tight Frame U-Nets demonstrated superior reconstruction quality over the standard U-Net by effectively mitigating streaking artifacts and preserving edge details.

The numerical results indicate that the Tight Frame U-Net is particularly effective, yielding better peak signal-to-noise ratio (PSNR) and structural similarity index (SSIM) scores. These architectures also demonstrated improved lesion detection capabilities, a crucial aspect in medical imaging.

Conclusion and Future Directions

The paper illustrates the potential of leveraging deep convolutional framelets for understanding and enhancing CNN architectures like U-Net. The proposed frame conditions and novel network designs mark a step towards optimizing neural networks for inverse problems, such as sparse-view CT.

Looking forward, the implications of this research extend to broader applications in AI and medical imaging. Future work could explore more sophisticated wavelet frames or adaptive mechanisms to further refine reconstruction performance across diverse imaging modalities and datasets. Additionally, extending these insights to other domains where data is sparse or noisy could prove to be highly beneficial.